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Math Help - Simplifying Radicals

  1. #1
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    Simplifying Radicals

    Please help me simplify these radicals.

    1)



    2)
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Simplifying Radicals

    What have you tried?

    1)
    Use basic rules like: \sqrt[n]{x^{a}}=x^{\frac{a}{n}} and a^{x}\cdot a^{y}=a^{x+y}
    2)
    The same over here, you have to know some basic rules like: (a-b)\cdot (a+b)=a^2-b^2 and (a+b)^2=a^2+2ab+b^2

    Try to use them where necessary and simplify.
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  3. #3
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    Re: Simplifying Radicals

    thank you. i will give it another try.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Simplifying Radicals

    Ok! You can show your work afterwards if you want .
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  5. #5
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    Re: Simplifying Radicals

    thanks for the help I did not put the "a" in a common root during the multiplication that was the error : )
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Simplifying Radicals

    I have simplified it this way:
    1)
    \sqrt[4]{a^{3}}+\sqrt[4]{a}\cdot \sqrt{a}+\frac{3\sqrt[4]{a^{9}}}{\sqrt{a^{3}}}
    =a^{\frac{3}{4}}+a^{\frac{1}{4}}\cdot a^{\frac{1}{2}}+\frac{3a^{\frac{9}{4}}}{a^{\frac{3  }{2}}}
    =a^{\frac{3}{4}}+a^{\frac{3}{4}}+3a^{\frac{3}{4}}=  5a^{\frac{3}{4}}}=5\sqrt[3]{a^{4}}
    2)
    (2\sqrt{7}-3)\cdot (2\sqrt{7}+3)-(\sqrt{7}+1)^2-(\sqrt{7}-2)^2
    [(2\sqrt{7})^2-9]-(7+2\sqrt{7}+1}-(7-4\sqrt{7}+4)=28-9-7-2\sqrt{7}-1-7+4\sqrt{7}-4=2\sqrt{7}
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